Ordinary, partial, and stochastic differential equations are derived from conservation laws and dynamical principles; analytical methods (separation, integrating factors, Green’s functions) are juxtaposed with numerical solvers (Runge–Kutta, multistep, shooting, finite-difference, finite-element), all tied together through stability, stiffness, and convergence proofs. Real-world case studies—oscillators, reaction–diffusion, and epidemiological SIR models—are integrated as executable Python notebooks.